Following formal notice that the 30-year-old had relinquished the title, he posted on X: “Thank you for the history.”
The WBA said the mandatory defence period for Pulev to meet Wardley will end on 4 April.
The winner must then defend against American Michael Hunter, who has won 24 of his professional bouts, before 25 October of this year.
Wardley came into boxing without an amateur background, having previously been a recruitment consultant in the City of London.
He made his professional debut in April 2017, on the same night as fellow Briton and current IBF heavyweight champion Daniel Dubois, albeit at different UK venues.